Getting Started

Installation

Add integrate to your Cargo.toml:

[dependencies]
integrate = "0.1"

Your First Integral

Let’s compute \(\int_0^1 e^x \, dx = e - 1 \approx 1.71828\) using the trapezoidal rule:

use integrate::newton_cotes::trapezoidal_rule;

let result = trapezoidal_rule(|x: f64| x.exp(), 0.0_f64, 1.0_f64, 1_000_usize);
println!("Result:   {:.6}", result);
println!("Exact:    {:.6}", std::f64::consts::E - 1.0);

Using the Prelude

For convenience, you can import all methods at once with:

use integrate::prelude::*;

This exposes all 11 integration functions directly.

Choosing a Method

You want to integrate…	Recommended method
A smooth function on \([a, b]\)	[`legendre_rule`] or [`trapezoidal_rule`]
A function with variable smoothness	[`adaptive_simpson_method`]
A smooth function to high precision	[`romberg_method`]
\(f(x)\,e^{-x}\) over \([0, \infty)\)	[`gauss_laguerre_rule`]
\(f(x)\,e^{-x^2}\) over \((-\infty, \infty)\)	[`gauss_hermite_rule`]
\(f(x)/\sqrt{1-x^2}\) over \([-1,1]\)	[`gauss_chebyshev1_rule`]
\(f(x)\sqrt{1-x^2}\) over \([-1,1]\)	[`gauss_chebyshev2_rule`]

Generics: f32 and f64

All Newton-Cotes and Romberg methods are generic over float types. You can pass f32 functions:

use integrate::newton_cotes::simpson_rule;

let result = simpson_rule(|x: f32| x * x, 0.0_f32, 1.0_f32, 1_000_usize);
println!("{:.6}", result); // ≈ 0.333333